solving the pendulum differential equation with a for loop

Question

federico midei 2020-9-12

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/592675-solving-the-pendulum-differential-equation-with-a-for-loop

评论： federico midei 2020-9-13

采纳的回答： BOB MATHEW SYJI

在 MATLAB Online 中打开

Hi I'm trying to write down a code that solves the equation of the pendulum in the hyp of little swings.

The task is to write it with a for loop without using the ODEs functions.

the code i wrote obviusly doesn't work.

Does someone could help me?

equation of pendulum:

l*diff(c,t,2)+g*c==0

code I wrote:

l=50; %rope length
g=9.81; %g constant
t=0; %time
syms c;
Dc= diff(c,t);
cond= [c(0)==0, Dc(0)==0.1]; %initial conditions
T=7.5*pi*sqrt(l/g);
n=linspace(0, T, 1000);
for i=1:n %I need the c value at every 't' from 0 to T with 1000 points
 t= i;
 ode = l*diff(c,t,2)+g*c==0;
 sol=dsolve(ode,cond);
  %sol=dsolve(ode);
  
end

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Answer 1

BOB MATHEW SYJI 2020-9-13

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/592675-solving-the-pendulum-differential-equation-with-a-for-loop#answer_493810

在 MATLAB Online 中打开

Hope this helps. The solution for the differential equation is obtained as cSol(t). The required solution is obtained as a row vector 'sol'

l=50; %rope length
g=9.81; %g constant
syms c(t);
Dc= diff(c,t);
ode = l*diff(Dc)+g*c==0;
cond=c(0)==0;
cond1=Dc(0)==0.1;
cSol(t)=dsolve(ode,[cond cond1]);
T=7.5*pi*sqrt(l/g);
n=linspace(0, T, 1000);
for i=1:length(n)
    sol(i)=double(cSol(n(i)));
end